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Interplay of symmetries and other integrability quantifiers in finite by Lakhsmanan Muthusamy

91 views · Published 7 September 2016 · 1:04:50 · Indexed 20 September 2026

Channel: International Centre for Theoretical Sciences · 2016 · Science & Technology

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DATES: Monday 29 Aug, 2016 - Tuesday 30 Aug, 2016

VENUE: Madhava Lecture Hall, ICTS Bangalore

Emmy Noether (1882­-1935) is well known for her famous contributions to abstract algebra and theoretical physics. Noether’s mathematical work has been divided into three ”epochs”. In the first (1908­-19), she made contributions to the theories of algebraic invariants and number fields. Her work on differential invariants in the calculus of variations, Noether’s theorem, has been called ”one of the most important mathematical theorems ever proved in guiding the development of modern physics”. In the second epoch (1920-­26), she began work that changed the face of abstract algebra. In her classic paper Idealtheorie in Ringbereichen (Theory of Ideals in Ring Domains, 1921) Noether developed the theory of ideals in commutative rings into a tool with wide­ranging applications. She made elegant use of the ascending chain condition, and objects satisfying it are named Noetherian in her honor. In the third epoch (1927­-35), she published works on noncommutative algebras and hypercomplex numbers and united the representation theory of groups with the theory of modules and ideals. In addition to her own publications, Noether was generous with her ideas and is credited with several lines of research published by other mathematicians, even in fields far removed from her main work, such as algebraic topology.

In ICTS-­TIFR, we shall celebrate the work of this remarkable mathematician and physicist in this two day discussion meet.

The topics will include the following:

Noether's Theorem in Classical Dynamics: Continuous Symmetries and Conservation Laws for physical systems.
Applications of Noether theorem in particle physics, condensed matter physics, gravity and string theory.
Noether's pioneering contributions to Commutative Algebra and other fields of pure mathematics.
Application deadline: 01 July, 2016

Support for train travel by students and postdocs will be provided as per rules. Due to limited funds, faculty applicants are requested to find an alternative travel support.

For more information, contact [email protected]

PROGRAM LINK: http://www.icts.res.in/discussion_meeting/lem2016/

Table of Contents (powered by https://videoken.com)
0:00:00 Start 
0:00:11 Interplay of symmetries and other integrable quantifiers in finite dimensional nonlinear dynamical systems
0:01:27 Objectives
0:03:20 Plan of talk
0:04:13 Dynamical System: Introduction
0:13:43 Point symmetries: Contd... 
0:16:20 Finding integrals
0:20:35 (a) Noether symmetries 
0:21:35 Noether symmetries: Contd... 
0:22:40 Noether symmetries: Contd... Example: 
0:23:44 Noether symmetries: Example Contd... 
0:24:42 (b) Contact symmetries
0:26:12 Contact symmetries: Contd... 
0:28:48 (c) X - Symmetries
0:29:58 Lambda- Symmetries: Contd... 
0:36:13 (d) Adjoint Symmetries (Bluman and Anco, Eur. J. App. Math. 1998)
0:36:21 Example
0:37:10 Ill Jacobi Last multiplier
0:40:54 Jacobi Last multiplier: Properties
0:42:35 Jacobi Last multiplier: Example
0:44:03 IV Darboux polynomial approach (G. Darboux,
0:47:12 Example
0:47:57 V Extended Prelle-Singer procedure
0:48:39 V Extended Prelle-Singer procedure for second order ODE
0:54:45 VI Interconnections
0:56:36 (b) Interconnections Contd...
0:57:41 Interconnections Contd... 
0:58:48 Interconnections Contd... (v) Darboux polynomial:
0:59:05 For second order ODEs
0:59:43 From Lie point symmetries to other quantifiers
1:00:05 From contact symmetries to other quantifiers
1:00:12 From Darboux polynomials to other quantifiers
1:00:16 From Jacobi last multipliers to other quantifiers
1:00:31 VII Higher order ODEs
1:01:08 VIII Conclusions

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